Exponential Stability of Pseudo Almost Periodic Solutions for Cellular Neural Networks with Multi-Proportional Delays

In this paper, Clifford-valued fuzzy neural networks with proportional delays, whose leakage term coefficients are also Clifford numbers, are considered. Based on the Banach fixed point theorem and differential inequality technique, we use a direct method to obtain the existence, uniqueness, and global attractivity of pseudo almost periodic solutions for the considered networks. Finally, we provide a numerical example to illustrate the feasibility of our results. Our results are new.

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Measure Pseudo Almost Periodic Solutions of Shunting Inhibitory Cellular Neural Networks with Mixed Delays

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2018.1561469 ◽

2019 ◽

Vol 40 (5) ◽

pp. 571-585 ◽

Cited By ~ 5

Author(s):

Mohsen Miraoui ◽

Nejib Yaakoubi

Keyword(s):

Neural Networks ◽

Periodic Solutions ◽

Cellular Neural Networks ◽

Mixed Delays ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Pseudo Almost Periodic Solutions ◽

Pseudo Almost Periodic

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Pseudo almost periodic synchronization of Clifford-valued fuzzy cellular neural networks with time-varying delays on time scales

Advances in Difference Equations ◽

10.1186/s13662-020-03041-w ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Yongkun Li ◽

Shiping Shen

Keyword(s):

Neural Networks ◽

Periodic Solutions ◽

Time Scales ◽

Discrete Time ◽

Cellular Neural Networks ◽

Fuzzy Cellular Neural Networks ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Pseudo Almost Periodic Solutions ◽

Pseudo Almost Periodic

Abstract At present, the research on discrete-time Clifford-valued neural networks is rarely reported. However, the discrete-time neural networks are an important part of the neural network theory. Because the time scale theory can unify the study of discrete- and continuous-time problems, it is not necessary to separately study continuous- and discrete-time systems. Therefore, to simultaneously study the pseudo almost periodic oscillation and synchronization of continuous- and discrete-time Clifford-valued neural networks, in this paper, we consider a class of Clifford-valued fuzzy cellular neural networks on time scales. Based on the theory of calculus on time scales and the contraction fixed point theorem, we first establish the existence of pseudo almost periodic solutions of neural networks. Then, under the condition that the considered network has pseudo almost periodic solutions, by designing a novel state-feedback controller and using reduction to absurdity, we obtain that the drive-response structure of Clifford-valued fuzzy cellular neural networks on time scales with pseudo almost periodic coefficients can realize the global exponential synchronization. Finally, we give a numerical example to illustrate the feasibility of our results.

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Global Exponential Stability of Weighted Pseudo-Almost Periodic Solutions of Neutral Type High-Order Hopfield Neural Networks with Distributed Delays

Abstract and Applied Analysis ◽

10.1155/2014/506256 ◽

2014 ◽

Vol 2014 ◽

pp. 1-17 ◽

Cited By ~ 2

Author(s):

Lili Zhao ◽

Yongkun Li

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Periodic Solutions ◽

Global Exponential Stability ◽

Neutral Type ◽

Distributed Delays ◽

Almost Periodic Solutions ◽

Almost Periodic ◽

Pseudo Almost Periodic Solutions ◽

Pseudo Almost Periodic

Some sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of weighted pseudo-almost periodic solutions to a class of neutral type high-order Hopfield neural networks with distributed delays by employing fixed point theorem and differential inequality techniques. The results of this paper are new and they complement previously known results. Moreover, an example is given to show the effectiveness of the proposed method and results.

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